A company's pricing schedule in the table below is designed to encourage large orders. $($A gross is $12$ dozen.$)$

$\backslash$table$[[q($order size, gross$),3,4,5,6],[p($price$/$dozen$),20,15,10,5]]$

$($a$)$ Find a formula for $q$ as a linear function of $p.$

$q=$

$($b$)$ Find a formula for $p$ as a linear function of $q.$

$p=$